Due to the rapidly widespread use of wireless equipment represented by mobile phones, demand for a filter prepared by combining a plurality of small and light-weight resonators increases. Conventionally, such wireless equipment was loaded mainly with a dielectric filter or a surface acoustic waves (SAW) filter. Recently however, filters including piezoelectric thin film resonators are loaded in many cases. The piezoelectric thin film resonator is low-loss in a high frequency region and at the same time advantageous from the viewpoint of the high power capability, electrostatic discharge (ESD) characteristic and the like. Further, by using the piezoelectric thin film resonator, a smaller monolithic filter can be provided.
Such piezoelectric thin film resonators include a FBAR (Film Bulk Acoustic Resonator) type and a SMR (Solidly Mounted Resonator) type. FIGS. 1-3 are cross-sectional views showing FBARs. Each of the FBARs is prepared by laminating on a substrate a laminate film mainly including an upper electrode, a piezoelectric film and a lower electrode. In each of the FBARs, a gap is formed below the lower electrode in a region where the upper electrode and the lower electrode oppose each other. The FBARs shown in FIGS. 1-3 are different from each other in the structures of the gaps.
The FBAR as shown in FIG. 1 includes a substrate 21, a lower electrode 22, a piezoelectric film 23, an upper electrode 24, and a dielectric film 25. The substrate 21 has a through hole 26 formed from the surface to the back face.
The FBAR as shown in FIG. 2 includes a substrate 41, a lower electrode 42, a piezoelectric film 43, an upper electrode 44 and a dielectric film 45. The substrate 41 has a cavity 46 formed on the surface.
The FBAR as shown in FIG. 3 has a substrate 31, a lower electrode 32, a piezoelectric film 33, an upper electrode 34 and a dielectric film 35. The FBAR is formed on the surface of the substrate 31.
FIG. 4 is a cross-sectional view showing a SMR. The SMR includes a substrate 51, a lower electrode 52, a piezoelectric film 53, an upper electrode 54 and an acoustic reflection film 56. The acoustic reflection film 56 is disposed under the lower electrode 52. The acoustic reflection film 56 is prepared by laminating alternately a film with low acoustic impedance and a film with high acoustic impedance. The film with low acoustic impedance and the film with high acoustic impedance each has a thickness of λ/4. Here, λ denotes a wavelength of an acoustic wave.
In the piezoelectric thin film resonator, when a high frequency electric signal is applied to the space between the upper electrode and the lower electrode, an acoustic wave is excited due to the inverse piezoelectric effect in the interior of the piezoelectric film sandwiched by the upper electrode and the lower electrode. Further, in the piezoelectric thin film resonator, a strain caused by the acoustic wave is converted to an electric signal due to the piezoelectric effect. In the FBAR, the acoustic wave is reflected on a face of the upper electrode being in contact with the air and on a face of the lower electrode being in contact with the air. In the SMR, the acoustic wave is reflected on a face of the upper electrode being in contact with air and on a face of the lower electrode being in contact with the acoustic reflection film. As a result, in the FBAR and SMR, thickness longitudinal acoustic waves having main displacement in the thickness direction occur. In the FBAR and SMR having the above-mentioned structures, a resonance occurs at a frequency where the total film thickness H of the laminate film part mainly formed with the upper electrode, the piezoelectric film and the lower electrode is the integral multiple (×n) of the ½ wavelength of the acoustic wave. The resonant frequency F can be calculated by substituting the film thickness H of the laminate film, a propagation velocity V of the acoustic wave depending on the materials, and the multiple n of the ½ wavelength of the acoustic wave, in the numerical formula below:F=nV/2H. 
This resonance phenomenon can be used to adjust the resonant frequency depending on the film thickness, thereby manufacturing a piezoelectric thin film resonator having a predetermined frequency characteristic. Further, a plurality of piezoelectric thin film resonators different from each other in the resonant frequency can be connected to manufacture a filter.
Cost reduction has been an object for a filter using a piezoelectric thin film resonator. In addition, with the trend for miniaturization of equipment loaded with a filter, smaller filters have been required. For meeting such requirements, reduction of a chip area without sacrificing the filter characteristics is considered seriously. In view of further miniaturization (reduction of area) of a chip with a filter element disposed, improvement in the arrangement of piezoelectric thin film resonators included in a filter will be required as well.
Document 1 (Proc. IEEE Ultrasonics Symposium, 2005, p. 101-104) discloses an arrangement and a structure of a piezoelectric thin film resonator included in a filter. In Document 1, in a piezoelectric thin film resonator included in a filter, the shape of a part where an upper electrode and a lower electrode sandwiching a piezoelectric film overlap (hereinafter referred briefly as an electrode shape) is a non-square and irregular polygon having no pairs of sides parallel to each other. This is for preventing occurrence of a transverse mode undesired wave in addition to the thickness longitudinal acoustic wave mainly utilized as mentioned above. The transverse mode undesired wave propagates in parallel to the electrode face, and is reflected on the electrode or the end of the gap. An undesired spurious may occur in the impedance characteristic of the piezoelectric thin film resonator as a result of exciting the transverse mode undesired wave. In a filter including a plurality of the piezoelectric thin film resonators, a ripple may occur in the passband.
Document 2 (JP 2000-332568 A) discloses a piezoelectric thin film resonator having an electrode shaped as a non-square and irregular polygon. The piezoelectric thin film resonator as disclosed in Document 2 can suppress harmful effects caused by the transverse mode undesired wave.